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1 Nuclear Instruments and Methods in Physics Research A 597 (28) 1 22 Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homepage: Air fluorescence relevant for cosmic-ray detection Summary of the 5th fluorescence workshop, El Escorial 27 Fernando Arqueros a,,jörg R. Hörandel b, Bianca Keilhauer c a Facultad de Ciencias Físicas, Universidad Complutense de Madrid, E-284 Madrid, Spain b Department of Astrophysics, Radboud Universiteit Nijmegen, P.O. Box 91, 65 GL Nijmegen, The Netherlands c Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 364, 7621 Karlsruhe, Germany article info Available online 23 August 28 Keywords: Fluorescence yield Air showers abstract High-energy cosmic rays with energies exceeding 1 17 ev are frequently observed by measurements of the fluorescence light induced by air showers. A major contribution to the systematic uncertainties of the absolute energy scale of such experiments is the insufficient knowledge of the fluorescence light yield of electrons in air. The aim of the 5th Fluorescence Workshop was to bring together experimental and theoretical expertise to discuss the latest progress on the investigations of the fluorescence light yield. The results of the workshop will be reviewed as well as the present status of knowledge in this field. Emphasis is given to the fluorescence light yield important for air shower observations and its dependence on atmospheric parameters, like pressure, temperature, and humidity. The effects of the latest results on the light observed from air showers will be discussed. & 28 Elsevier B.V. All rights reserved. 1. Introduction The Earth is permanently exposed to a vast flux of particles from outer space. Most of these particles are fully ionized atomic nuclei, covering a large range in energy from the MeV regime to energies above 1 2 ev. In 1962 the first event with an energy exceeding 1 2 ev was recorded [1]. Such cosmic rays are the highest-energy particles in the Universe, carrying the (macroscopic) energy of about 5 J concentrated on a single nucleus. Since their first discovery more than 4 years ago their origin has been an open question. How do cosmic accelerators work and what are they accelerating? is one of 11 science questions for the new century asked by the National Research Council of the National Academies of the United States [2], underlining the importance of this topic to astroparticle physics. The properties of cosmic rays at highest energies are investigated with various experiments [3 6]. The flux of cosmic rays with energies exceeding 1 2 ev is below 1 particle per square kilometer and century. Thus, a reasonable measurement of these particles requires huge detectors operated stably over long periods of time. At present, this can be realized only with ground based experiments, registering the secondary particles generated by high-energy cosmic rays in the atmosphere. When a highenergy cosmic ray enters the Earth s atmosphere it induces a cascade of secondary particles, an extensive air shower. By far the Corresponding author. Tel.: ; fax: address: arqueros@gae.ucm.es (F. Arqueros). most abundant particles in air showers are photons, electrons, and positrons, comprising the electromagnetic shower component. On their way through the atmosphere the (relativistic) charged particles emit Cherenkov radiation and excite nitrogen molecules to emit fluorescence light. A small fraction of the secondary particles eventually reaches the observation level. Over time, several methods to measure extensive air showers have been established. They can be divided into two groups: experiments measuring secondary particles (electrons, muons, and hadrons) reaching ground level and detectors observing the emitted Cherenkov or fluorescence photons. The latter allow for a threedimensional reconstruction of the shower profile in the atmosphere. A critical issue for all experiments is to establish an absolute energy scale for the measured showers. For experiments registering secondary particles at ground level this usually involves the usage of simulations of the shower development in the atmosphere, thus, introducing systematic uncertainties due to our limited knowledge of the hadronic interactions at such high energies. On the other hand, fluorescence measurements of air showers provide a calorimetric measurement of the energy deposited in the air, being (nearly) independent of air shower simulations. The deposited energy is assumed to be proportional to the energy of the primary, shower inducing, particle. At present, this is the most direct and model independent method to determine the energy of an air shower. The main systematic uncertainty of this method arises from the insufficient knowledge of the fluorescence light yield of electrons in air. However, this is a quantity which can be /$ - see front matter & 28 Elsevier B.V. All rights reserved. doi:1.116/j.nima

2 2 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) 1 22 measured in laboratory experiments, injecting electrons into air targets. Responsible for the fluorescence emission of the nitrogen molecules is mainly the electromagnetic shower component. The critical energy of electrons in air is about 84 MeV, thus, the bulk of particles has energies easily accessible at accelerators, or, at lower energies, even through radioactive b-decays. This is the main focus of the present article. It gives an overview on the actual status of the knowledge of the fluorescence light yield of electrons in air, important for air shower detection. It summarizes the results of the 5th Fluorescence Workshop, which was held in El Escorial, Spain from September 16th to 2th, 27. After a short overview on the principle of the detection of air showers using fluorescence light (Section 2.1), experiments applying this technique to register cosmic-ray induced air showers are described (Section 2.2). The main physical processes involved in the production of fluorescence light in air are reviewed in Section 3. Contemporary experimental tools and theoretical treatments are discussed in Section 4. Latest data are compiled in Section 5, paying special attention to the dependence of the fluorescence light yield on atmospheric parameters, such as pressure, temperature, and humidity. In the following section (Section 6) the influence of the results obtained on the light yield in air showers developing in realistic atmospheres is discussed. An outlook describing the next steps in determining the fluorescence yield in air concludes the article (Section 7). The most important pioneering measurements of the fluorescence light yield are summarized in an accompanying article [7]. 2. The fluorescence technique 2.1. Principle of air shower detection with fluorescence light A high-energy cosmic ray entering the atmosphere induces a cascade of secondary particles. One way to determine the energy of the primary particle is to measure the energy deposited in an absorber (i.e. the atmosphere), this is called a calorimetric energy measurement (e.g. Ref. [8]). If the shower is absorbed completely, the energy of the primary particle is identical to the energy deposited. However, in an air shower some energy is escaping a calorimetric measurement: a fraction of secondary particles reaches ground level and some energy is carried away by invisible particles such as neutrinos. Luckily, corrections for this effect are small and rather model independent, as will be discussed below. The calorimetric measurement by means of fluorescence light detection uses the fact that secondary particles in showers (mostly electrons and positrons) deposit energy in the atmosphere by ionization or excitation of air molecules. The excited nitrogen molecules subsequently relax to their ground state partially by the emission of fluorescence photons. The light is emitted isotropically, which implies that showers can be viewed from the side, thus, telescopes can observe large fiducial volumes of air. Most of the fluorescence light is emitted in the near UV region with wavelengths between about 3 and 4 nm. Simulation studies show that most of the energy deposited into the atmosphere arises from electrons (and positrons) with energies below 1 GeV with a maximum at about 3 MeV [9]. It is commonly assumed that the number of emitted fluorescence photons is proportional to the energy deposited in the atmosphere. The number of fluorescence photons dn g which are generated in a layer of atmosphere with thickness dx registered by a fluorescence detector can be expressed as Z dn g dx ¼ d 2 N g dx dl t atmðl; XÞ FD ðlþ dl. (1) FD denotes the efficiency of the fluorescence detector and t atm the transmission of the atmosphere. The latter includes all transmission losses due to optical absorption, Rayleigh scattering, and Mie scattering from the point of emission to the detector. The number of emitted fluorescence photons dn g emitted per wavelength interval dl and matter traversed dx is obtained as d 2 N Z g dx dl ¼ Yðl; P; T; u; EÞ dn eðxþ de dep de. (2) de dx The energy spectrum of the electrons (and positrons) at an atmospheric depth X is given by dn e ðxþ=de and de dep =dx describes the energy deposited in a layer of atmosphere with thickness dx. The fluorescence light yield 1 Y describes the number of emitted photons per deposited energy (photons per MeV). For a calorimetric measurement we are interested in the deposited energy, thus, this definition relates the searched quantity directly to the observed amount of light. In the literature Y is frequently given in units of photons per meter (or photons per unit length). This definition has the disadvantage that the number of photons emitted per unit length changes with varying air density. It is nontrivial to convert the two quantities into each other. Throughout this article we use the definition of photons per deposited energy, unless noted otherwise. The fluorescence light yield Y at a wavelength l depends on the atmospheric pressure P, the temperature T, the humidity u, and, in principle, as well on the energy of the electrons E. If the light yield is assumed to be energy independent, it can be taken out of the integral yielding d 2 N g dx dl ¼ Yðl; P; T; uþdetot dep dx. (3) The total energy deposited in an atmospheric layer with thickness dx is written as de tot Z dep dx ¼ dne ðxþ de dep de. (4) de dx With Eq. (1) the relation Z dn g dx ¼ detot dep Yðl; P; T; uþt atm ðl; XÞ FD ðlþ dl (5) dx is obtained. It shows that the number of fluorescence photons detected is proportional to the energy deposited in the atmosphere. It remains to be shown that the fluorescence yield is indeed independent of the electron energy, see Section To calculate the energy of the primary particle from the observed fluorescence light still some corrections are necessary. The observed light contains also a contamination of Cherenkov light, either direct light (mostly emitted in forward direction) or scattered light. This effect has to be corrected for on an event-toevent basis [1]. It has to be taken into account that the cascade is not absorbed completely in the atmosphere and secondary particles reach ground level (longitudinal leakage of the calorimeter). Furthermore, particles which are not detected (neutrinos, high-energy muons) carry away energy. This invisible energy depends slightly on the mass of the primary particle and the hadronic interaction model used to describe the shower development in the atmosphere. Investigations of the Auger Collaboration indicate that the correction factor varies between 1.7 and 1.17 only, assuming primary protons or iron nuclei and applying different hadronic interaction models [11]. For illustration, we discuss here the systematic uncertainties of the absolute energy scale of the Pierre Auger Observatory 1 In contrast to later on, we use in this section the fluorescence yield per unit wavelength interval.

3 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) (as evaluated before the 5th Fluorescence Workshop) [12]. The fluorescence telescopes are end-to-end calibrated using a large homogeneous light source which leaves an uncertainty of 9.5%. Uncertainties in the shower reconstruction contribute with 1% and the correction of the invisible energy adds another 4% to the error budget. The atmospheric profile above the observatory is regularly monitored [13]. However, an uncertainty of about 4% for the energy scale of an individual event remains. In addition, uncertainties related to the fluorescence yield have to be taken into account. The dominant contribution is due to the absolute light yield (14%). The dependence on atmospheric parameters contributes with 7%. This results in a total systematic uncertainty of 22%. Values for other experiments are similar and confirm that the biggest uncertainty for the absolute energy scale is the insufficient knowledge of the fluorescence yield Yðl; p; T; uþ. To review the latest progress on the determination of this value is the objective of the present article Air shower experiments applying the fluorescence technique In the following, the principle set-ups of air shower detectors applying the fluorescence technique are briefly sketched. Illustratively, a fluorescence detector for such an experiment has to be able to observe a 1 W light bulb 2 moving at the speed of light through the atmosphere watched from a distance of 3 km. To realize this, large-aperture telescopes are used to focus the light on cameras equipped with fast photomultiplier tubes, sensitive in the near UV region. 3 First ideas to use the Earth s atmosphere as vast scintillation detector were discussed in the early 196s [14]. The early history of experiments applying the fluorescence technique is summarized elsewhere [15] Initial experiments The pilot experiment to study the feasibility of detecting air showers with the fluorescence technique was the Cornell Wide Angle System proposed and built by K. Greisen and colleagues in the 196s [16]. It consisted of three detector stations set up in the vicinity of the Cornell University campus. Each station comprised five photomultiplier tubes in a hexahedron arrangement, with a tube pointing north, south, east, west, and upward, respectively. The four radial tubes were tilted upwards by 31. The system was operational for about 1 h. Light flashes were recorded, but they could not be attributed to air showers beyond doubt. In 1967, a full scale fluorescence experiment was constructed by Greisen s group. It comprised 5 photomultiplier tubes, each corresponding to a pixel with a solid angle of.1 sr. The photomultipliers were divided into 1 modules, each of them was equipped with a :1m 2 Fresnel lens. The experiment was operated for several years but was not sensitive enough to detect high-energy cosmic rays. Similar activities were conducted by the Tokyo group leading to the INS-Tokyo experiment. In 1969 they recorded first clear fluorescence light signals from an extensive air shower with an energy exceeding ev [17] The Fly s eye experiment In 1976 physicists from the University of Utah detected fluorescence light from cosmic-ray air showers. Three prototype modules were used at the site of the Volcano Ranch air shower array near Albuquerque, New Mexico. Each module comprised a 2 The fluorescence light of a 1 17 ev shower corresponds to a light bulb of about 1 W. 3 Recent results of air shower experiments applying the fluorescence technique are summarized in e.g. Refs. [3 6]. 1.8 m diameter mirror for light collection with a camera consisting of 14 photomultiplier tubes at the focal plane. Fluorescence light was recorded in coincidence with an air shower array. These prototypes led eventually to the development of the Fly s Eye detector. The Fly s Eye observatory [18] consisted of two stations, separated by 3.3 km. The first one (Fly s Eye 1) comprised 67 front aluminized spherical section mirrors, with a diameter of 157 cm. Winston light collectors and photomultipliers were hexagonally packed in groups of either 12 or 14 light sensing units, or eyes mounted in the focal plane of each mirror. The photomultipliers (EMI 9861B) had a fairly uniform quantum efficiency over the spectral range from 31 to 44 nm. A motorized shutter system kept the eyes both light tight and weather proof during the day and permitted exposure to the sky at night. Each mirror unit was housed in a single, motorized corrugated steel pipe about 2.13 m long and 2.44 m in diameter. The units were turned down with mirror and open end facing the ground during the day and turned up at night to a predetermined position so that each eye observed an angular region of the sky. In total, 88 eyes were observing the complete upper hemisphere. The projection of each hexagonal eye onto the celestial sphere resembles the compound eye of an insect, hence, the name Fly s Eye. The second telescope (Fly s Eye II) was a smaller array of identical units, with 12 eyes in total, observing roughly one azimuthal quadrant of the night sky with elevation angles ranging between 21 and 381 above the horizon. Whenever the first telescope recorded an event, it sent an infrared flash of light towards the second telescope, which recorded pulse integrals and arrival times. The shower track geometry was reconstructed either from hit patterns and timing information by a single Fly s Eye detector or by stereoscopic viewing and relative timing by both Fly s Eyes. The experiment has been operated between 1981 and For the first time the fluorescence technique has been applied successfully to explore the properties of ultra high-energy cosmic rays on a large scale The HiRes experiment The High Resolution Fly s Eye experiment (HiRes) was located in Utah, USA (4 N, 112 W) [19]. It was the successor of the Fly s Eye experiment. HiRes consisted of two detector sites (Hires I and II) separated by 12.6 km, providing almost 361 azimuthal coverage, each. Both telescopes were formed by an array of detector units. The mirrors consisted of four segments and formed a 5:1m 2 spherical mirror. At its focal plane an array of photomultiplier tubes was situated, viewing a solid angle of HiRes I consisted of 22 detectors, arranged in a single ring, overlooking between 31 and 171 in elevation. This detector used an integrating ADC read-out system, which recorded the photomultiplier tubes pulse height and time information. HiRes II comprised 42 detectors, set up in two rings, looking between 31 and 311 in elevation. It was equipped with a 1 MHz flash ADC system, recording pulse height and timing information from its phototubes. The experiment has been operated between 1997 and Telescope Array The Telescope Array is an air shower experiment in the West Desert of Utah (USA), 14 miles south of Salt Lake City (39.31N, W) [2]. It comprises 576 scintillator stations and three fluorescence detector sites on a triangle with about 35 km separation. Each fluorescence detector station is equipped with telescopes, viewing 3 33 in elevation and 18 in azimuth [21]. The telescopes have a segmented spherical mirror with a diameter of 3.3 m and a focal length of 3. m. Each

4 4 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) 1 22 telescope has a camera comprising 256 photomultiplier tubes (Hamamatsu R958), corresponding to a pixel size of about 11 each. The sensitive area of a camera is 1 m 1 m, which corresponds to a field of view of 151 in elevation and 181 in azimuth. The photomultipliers are read out by a FADC system. The experiment has been taking data since The Pierre Auger Observatory The observatory combines the observation of fluorescence light with imaging telescopes and the measurement of particles reaching ground level in a hybrid approach [22]. The southern site (near Malargüe, Argentina, 35.21S, 69.51W, 14 m above sea level) of the worlds largest air shower detector consists of 16 water Cherenkov detectors set up in an area covering 3 km 2. Four telescope systems overlook the surface array. A single telescope system comprises six telescopes, overlooking separate volumes of air. Each telescope is situated in a bay, protected by a remotely operated shutter. Light enters the bay through an UV transmitting filter and a ring of corrector lenses. A circular diaphragm (2.2 m diameter), positioned at the center of curvature of a spherical mirror, defines the aperture of the Schmidt optical system. A 3:5m 3:5 m spherical mirror focuses the light onto a camera with an array of 22 2 hexagonal pixels. Each pixel is a photomultiplier tube, complemented by light collectors. Each camera pixel has a field of view of approximately 1.51 in diameter. A camera overlooks a total field of view of 3 azimuth 28:6 elevation. The photomultiplier signals are read out by FADC systems. The observatory has been completed in 28 and has been taking data stably with a growing number of detector stations since 24. Presently (28), the Pierre Auger Collaboration is extending the observatory to lower energies. For this objective additional high-elevation telescopes (HEAT, High Elevation Auger Telescopes) are being built, covering an angular range from 31 to 61 in elevation [23]. These telescopes will be operated with an additional infill array of surface detectors combined with underground muon counters (AMIGA, Auger Muons and Infill for the Ground Array) [24] and antennae to detect radio emission from air showers [25]. To complete and extend the investigations begun in the South, the Pierre Auger Collaboration presently prepares an observatory in the northern hemisphere in Colorado, USA [26]. The set-up will, similarly to the southern site, comprise water Cherenkov detectors and fluorescence telescope systems. 3. Physical processes involved in the generation of airfluorescence light Electrons passing through the atmosphere deposit energy due to inelastic collisions with air molecules. A small fraction of them give rise to the production of the fluorescence light observed in the spectral range of interest (29 43 nm). This air-fluorescence light is produced by nitrogen molecules. In this section the main features of the excitation and deexcitation of N 2 molecules will be reviewed (Section 3.1). Fluorescence quenching including the humidity effect will also be discussed (Section 3.2). Finally, the definition of the various parameters associated with the fluorescence yield as used in the literature will be presented (Section 3.3) Electron excitation and radiative de-excitation A scheme of the molecular levels of N 2 and N þ 2 is shown in Fig. 1. As is well known from elementary molecular physics, each electronic state is split in vibrational levels v. In addition, each vibrational level is split in rotational sub-levels following a complicated structure. Electron collision excites molecular nitrogen in the ground state to upper levels. Down going arrows in Fig. 1 represent the de-excitation processes giving rise to fluorescence radiation. Although transitions take place between individual rotational levels of the upper and lower states, the corresponding rotational structure of the molecular spectrum is not resolved in our experiments. Under moderate spectral resolution, transitions between vibrational levels give rise to molecular bands v v with a spectral width and shape determined ASHRA The All-sky Survey High Resolution Air-shower (ASHRA) telescope is a proposed detector system to simultaneously measure Cherenkov and fluorescence light on the entire sky with 1 arc min resolution [27]. It is planned to install two stations at a distance of about 3 4 km on an island in Hawaii. A station comprises 12 wide-angle telescopes. Each telescope has a field of view of 5 5, read out by CMOS sensor arrays JEM-EUSO JEM-EUSO is a proposed super-wide field UV telescope to detect ultra high-energy cosmic rays with energies above 1 2 ev [28]. It will be attached to the International Space Station (ISS) and will observe fluorescence photons emitted by air showers from an orbit of about 43 km altitude. The three-dimensional development of the shower is reconstructed from a series of images of the shower. The spatial resolution is about :75 :75 km 2. A double Fresnel lens module with 2.5 m diameter is the baseline optics for the JEM-EUSO telescope. The focal surface is equipped with about 6 multi-anode photomultipliers. The launch is planned for 212. Fig. 1. Molecular levels of N 2 and N þ 2. Broad arrows represent the main transitions (1N and 2P systems) [16].

5 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) Fig. 2. Air-fluorescence spectrum excited by 3 MeV electrons at 8 hpa as measured by the AIRFLY Collaboration [32]. by the rotational structure. 4 The set of bands connecting a given pair of electronic states is named a band system. In our spectral range, nitrogen fluorescence comes basically from the Second Positive system C 3 P u! B 3 P g of N 2 and the First Negative system B 2 S þ u! X2 S þ g of Nþ 2 (see Fig. 1) whichintheairfluorescence community are usually denoted as 2P and 1N systems, respectively. Notice that while the 2P system is generated after the N 2 X 1 S þ g! C3 P u excitation, 1N fluorescence takes place as a consequence of the X 1 S þ g!ðnþ 2 ÞB2 S þ u molecular ionization, leaving the nitrogen ion in a specific excited state. The wavelengths of the molecular bands of nitrogen are well known (see for instance Ref. [3]). Apart from the 1N and 2P systems the weak bands of the N 2 Gaydon Herman (GH) system have been observed in the airfluorescence spectrum [29,31]. A spectrum typically observed at high pressure between 28 and 43 nm for air is depicted in Fig. 2 [32]. The labels mark 21 major transitions. All important transitions and the corresponding wavelengths between 29 and 43 nm are compiled in Table 1. The cross-section for excitation of the upper electronic levels of both systems as a function of electron energy is displayed in Fig. 3. The curve for the 2P system shows a sharp maximum at about 15 ev followed by a fast E 2 decrease, as expected from the optically forbidden nature of this transition. On the contrary, the excitation cross-section for the 1N system shows a much softer maximum at about 1 ev followed by a much slower ðlog EÞ=E decrease which becomes a soft growing behavior at relativistic energies [33,34]. For a given electronic state the cross-section for the excitation to a vibrational level v is proportional to the Franck Condon factor q X!v, defined as the overlapping integrals between the vibrational wave functions of the lower and upper levels of the excitation process. The Einstein coefficients A vv give the probability per unit time of radiative de-excitation v v. Therefore, the probability of emission of a fluorescence v v photon by electron impact is proportional to the optical cross-section defined as A s vv ¼ s vv v P v A ¼ s v B vv vv 4 See e.g. Ref. [29] for some illustrative examples. (6) Table 1 Transitions and corresponding wavelengths of the air-fluorescence spectrum [32] Transition and therefore, in the absence of other effects, the relative intensity of a molecular band with respect to a reference transition (e.g. ) of the same system is given by I vv I ¼ s vv s ¼ q X!v l (nm) 2P(3,1) P(2,) GH(6,2) 32. GH(5,2) 38. 2P(3,2) P(2,1) P(1,) GH(6,3) P(4,4) P(3,3) P(2,2) P(1,1) P(,) GH(,4) P(2,3) 35. 2P(1,2) P(,1) GH(,5) P(3,5) P(2,4) P(1,3) P(,2) P(4,7) GH(,6) N(1,1) N(,) P(2,5) P(1,4) P(,3) 45. 2P(3,7) P(2,6) 42. 1N(1,2) P(1,5) N(,1) B vv. (7) q X! B

6 6 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) shortened as compared with the radiative one as 1 t v ¼ 1 t r v þ 1 t c v (12) σ exc (m 2 ) Tabulated values for both parameters q X!v and A vv are available in the literature [35,36]. The relative intensities between bands of different systems can also be predicted using the relative values of the corresponding excitation cross-sections. Transition probabilities determine the radiative lifetime t r of the excited level 1 t r ¼ A v ¼ X A vv. (8) v v Notice that, as shown below, in a laboratory experiment both relative intensities (7) and lifetime (8) have to be corrected by the effect of collisional quenching Fluorescence quenching At high pressure, molecular de-excitation by collision with other molecules of the medium plays an important role (collisional quenching). At a given temperature, the corresponding transition probability A v c is proportional to the collision frequency and, thus, to the gas pressure P. The characteristic pressure P v is defined as the one for which the probability of collisional quenching equals that of radiative de-excitation A c v ðp v Þ¼A v, A c v ðpþ ¼A P v. (9) P v C 3 Π u E (ev) B 2 Σ + u Fig. 3. Total cross-sections for the excitation of the electronic states C 3 P u and B 2 S þ u versus electron energy [34]. Thus, the fluorescence intensity in the absence of quenching I vv is reduced by the Stern Volmer factor [37] I vv ðpþ ¼I 1 vv 1 þ P=P. (1) v From Eqs. (7) and (1) the relative intensities of molecular bands at high pressure ðpbp Þ become 5 I vv ¼ q X!v B vv P v I q X! B P. (11) Collisional quenching enlarges the total transition probability and, therefore, the lifetime of the population of excited molecules t v is 5 Experimental confirmation of a collisional mechanism populating vibrational levels of the C 3 P u state which might induce an additional pressure dependence of the 2P relative intensities has been shown in Refs. [38,39]. with t c v ¼ 1=Ac v. As a result, the effective lifetime decreases with pressure as 1 t v ðpþ ¼ 1 t r 1 þ P v P. (13) v Both t r v and P v can be measured in a plot of reciprocal lifetime versus pressure (Stern Volmer plot). This is a very well established technique in use since many years for the experimental determination of radiative lifetimes and quenching cross-sections. In principle, a measure of the fluorescence intensity versus pressure (1) also provides a determination of P v. However, as discussed in detail later, in a laboratory experiment the above relationship might be distorted because of the effect of secondary electrons leading to systematic uncertainties in the measurement of the characteristic pressures. The probability of collisional de-excitation per unit time of a molecule in a given upper level v can be expressed 6 in terms of the quenching rate constant K Q as A c ¼ NK Q where N is the number of molecules per unit volume. In the case of pure nitrogen K Q ¼ s NN v (14) and rffiffiffiffiffiffiffiffiffiffiffi 16kT v ¼ (15) pm where s NN is the cross-section for collisional de-excitation between nitrogen molecules, v is the mean value of the relative velocity of molecules in the gas, T is the absolute temperature, M is the molecular nitrogen mass, and k is the Boltzmann s constant. Since P ¼ NkT, the characteristic pressure for pure nitrogen can be expressed as P N ¼ kt pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 t s NN v ¼ pmkt 1 4s NN t r. (16) The above expressions can be generalized for a mixture of gases as 1 P ¼ X f i P (17) i i where f i is the fraction of molecules of type i in the mixture and P i ¼ kt 1. (18) t s Ni v Ni In the general case, the relative velocity v Ni is given by [4] sffiffiffiffiffiffiffiffi 8kT v Ni ¼ (19) pm where m ¼ M N M i =ðm N þ M i Þ is the reduced mass of the two body system N i. For dry air the above sum includes basically nitrogen and oxygen with f N ¼ :79 and f O ¼ :21. However, in practice, air contains also other components. For instance, the effect of argon can be treated by Eqs. (17) and (18) accordingly. A particular interesting case is the effect of water vapor. The characteristic pressure of humid air P hum containing a fraction f H2O of water molecules, that is a water vapor pressure 6 In the next paragraphs all collisional parameters will be assumed to correspond to a given molecular level v.

7 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) P H2 O ¼ Pf H2 O, is related with that of dry air P dry by 1 P ¼ 1 hum P 1 P H2O þ P H2O 1 dry P P P. (2) H 2 O Laboratory measurements of P for nitrogen with variable quantities of water vapor, argon, oxygen, etc. provide values of the corresponding P i pressures and, therefore, the dependence of fluorescence intensity on environmental conditions. Quenching collision is a very complex problem of molecular physics and basically no reliable theoretical predictions on crosssections are available. Therefore, a description of the dependence of fluorescence quenching on pressure and humidity relies on experimentally determinated P values. Furthermore, fluorescence quenching depends on temperature for a given density and air composition. Firstly, the frequency p ffiffiffi of collisions increases with v and, thus, P grows with T (16). Secondly, the collisional cross-section is a function of the kinetic energy of the colliding particles and, thus, s Ni is a function of T. While the first dependence obeys well known laws of the kinetic theory of gases, the second one is again associated to the molecular problem of collisional de-excitation, in this case on the dependence of the quenching cross-section on collision energy. Very few experimental studies of the temperature dependence for nitrogen fluorescence are available. On the other hand, no simple theory has been developed capable to predict the temperature dependence of quenching. The collisional crosssection is assumed to follow a power law in temperature, 7 s / T a, where the a-parameter might be either positive or negative, depending on the nature of the partners and the type of interaction. The a-coefficient might even be valid only for certain temperature ranges, since the dominating type of interaction varies with the velocity of the molecules. As a consequence, from Eq. (1) a dependence of fluorescence intensity as 1 I / 1 þ bta 1=2 (21) can be predicted for a temperature scan at constant pressure, while the dependence at constant gas density r ¼ P=ðR gas TÞ (R gas is the specific gas constant) follows: 1 I / 1 þ b T aþ1=2 (22) where b and b are constants. In this volume new interesting measurements of the T dependence for pure nitrogen [41] and air [44] will be presented Fluorescence yield Several parameters can be used to quantify the intensity of airfluorescence radiation in regard with the energy deposited by electrons. In addition, the same physical magnitudes are denominated in the literature with different names and/or using different symbols. The main physical magnitudes are the following: Number of fluorescence photons emitted per unit electron path length. Several authors (for instance Refs. [34,45 48]) name it fluorescence (or photon) yield. Fraction of deposited energy emitted as fluorescence radiation (without units) named fluorescence efficiency in Refs. [45 47]. Number of fluorescence photons emitted per unit deposited energy. For several authors (for instance Refs. [29,49,5]) this parameter is the fluorescence yield. 7 See Refs. [41 43] for discussions on the T dependence of the quenching cross-section. In this article we will use the following definitions and symbols: l ðm 1 Þ is the number of fluorescence photons with wavelength l corresponding to a given transition v v 8 per unit of electron path length. F l is the fluorescence efficiency, defined as the fraction of deposited energy emitted as fluorescence radiation. The fluorescence yield Y l ðmev 1 Þ is defined as the number of fluorescence photons emitted per unit deposited energy. The ratio of F l and Y l is easily given by the energy of the photons E l ¼ hn with n ¼ c=l. However, the relationship between l and Y l is not straightforward. As discussed below, fluorescence light is basically generated by secondary electrons produced in ionization processes. These secondaries have a non-negligible range and, therefore, measured fluorescence intensity depends on geometrical features of the observation volume. A precise measurement of the fluorescence yield requires the evaluation of deposited energy in the same gas volume from where fluorescence is being detected. The total number l of fluorescence photons generated per unit path length in a very large medium can be expressed as a function of the optical cross-section s l of the transition by [34] s l ¼ N l 1 þ P=P (23) l where N is the density of nitrogen molecules and P l is the characteristic pressure of the upper level v of the transition. Obviously, l depends on electron energy because of the energy dependence of the optical cross-section. In a laboratory experiment with a finite observation volume, a fraction 9 of these photons is not detected by the system. Eq. (23) can be applied using an effective optical cross-section s eff l as defined in Ref. [33]. The number of fluorescence photons per unit column density per electron is given by l ¼ N A s eff l A r M gas 1 þ P=P ¼ l l 1 þ P=P (24) l where r is the gas density, N A is Avogadro s number and M gas is the mass of the gas molecules. The value of l =r in the absence of quenching ðp ¼ Þ is named A l in Refs. [45,46]. The fluorescence efficiency depends on pressure as F l ¼ F 1 l 1 þ P=P. (25) l At zero pressure, F l is given by F l ¼ ra l hn (26) ðde=dxþ dep where ðde=dxþ dep is the energy deposited per unit electron path length in the same volume where fluorescence photons have been generated (see below for more details on the effect of secondary electrons). Finally, the fluorescence yield follows the same pressure dependence as F l : Y l ¼ Y 1 l 1 þ P=P (27) l 8 In the next paragraphs, until the end of this section, the wavelength l will characterize the molecular transition instead of the vv pair. This is a more compact notation very common in articles of the air-fluorescence community. 9 This fraction depends on the gas pressure and the geometrical features of the experimental set-up.

8 8 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) 1 22 and its value in the absence of quenching is given by Y l ¼ F l hn. (28) Eqs. (27) and (28) can be written as [45,46] 1 ra Y l ¼ l p ffiffiffi (29) ðde=dxþ dep 1 þ rb l T where B l ¼ R pffiffiffi gas T P. (3) l The dependence of the fluorescence yield on pressure, temperature, humidity, etc. can be predicted from either Eqs. (27) and (28) or (29), using the characteristic pressure as given above in Eqs. (17) and (18). 4. The actual status This section describes the progress in the last few years on the experimental and theoretical tools developed for air-fluorescence studies. In Section 4.1 the modern experimental techniques used for the measurement of fluorescence yield and its dependence on atmospheric parameters are described. Electron sources, target features, detection systems as well as the various techniques developed for the absolute calibration of the systems are described. Finally, in Section 4.2 theoretical results on the processes leading to the emission of air-fluorescence light and the relation to deposited energy are discussed Experimental techniques beam of the 15-ID line of this accelerator produces an almost monochromatic beam of electrons through photoelectric and Compton interactions with the ambient air. Also at the Argonne National Laboratory, the Chemistry Division electron Van de Graaff accelerator operated in pulsed mode at 6 Hz, with beam currents from.2 to :8 ma, was used by this collaboration to get electrons in the range.5 3 MeV. Measurements in the energy range from 3 to 15 MeV were performed at the Argonne Wakefield Accelerator. The LINAC was operated at 5 Hz, with bunches of maximum charge of 1 nc, length 15 ps (FWHM), and a typical energy spread of :3 MeV at 14 MeV. Finally, measurements in the energy region 5 42 MeV were performed by AIRFLY at the Beam Test Facility of the INFN Laboratori Nazionali di Frascati, which can deliver electrons with intensity ranging from single particle up to about 1 particles per bunch at a repetition rate of 5 Hz with a typical pulse duration of 1 ns Radioactive sources. Beta emitters provide electrons with a continuous energy spectrum. In particular, 9 Sr 9 Y sources with a maximum and average energy of 2.3 and.85 MeV, respectively, are widely used. This energy range, around the minimum of the energy loss curve, is of great interest in air-fluorescence studies. In this technique fluorescence detection is based on electron photon coincidences. A schematic drawing of the chamber used by Nagano et al. [46] applying this technique, is presented in Fig. 4. An advantage of using radioactive sources is that once the source is safely located in the experimental set-up, long lasting experiments can be carried out at very low maintenance costs. However, this technique has also some disadvantages. The main one is that unless strong radioactive sources are used, the rate of coincidences is very low and, thus, very large data acquisition Any experimental set-up consists basically of three components: a source of electrons (or a-particles) properly monitored, a collision chamber where air or any gas mixture is excited by the electrons, and an optical as well as an electronic system to register the fluorescence light intensity Electron sources Three types of sources are used in air-fluorescence experiments: electron beams from accelerators in large facilities, radioactive sources, and low-energy electron guns in laboratories. Gas in photomultiplier tube filter quartz window window of size 2.5cmφ shutter Accelerators. They can provide electron beams with a small diameter typically of about few millimeters. Different kinds of accelerators are available for the various energy ranges (kev GeV). In particular, they are the only possible source for very highenergy electrons. A disadvantage of this technique is the large background signal induced in the fluorescence detectors which requires a careful subtraction from the fluorescence signal. Furthermore, electrons exit the accelerator line through a window of a certain thickness and material dependent on the energy range. The FLASH Collaboration [48,49,51] used the Final Focus Test Beam facility at the Stanford Linear Accelerator Center which provided 28.5 GeV electrons in 3 ps pulses of about 1 8 electrons at a rate of 1 Hz. The MACFLY Collaboration [52] used the CERN/SPS-X5 test beam facility which delivers a pulsed electron beam of about 1 4 electrons per spill (4.8 s duration) every 16.8 s. Measurements at 2 and 5 GeV were carried out using this facility. The AIRFLY Collaboration exploits this technique in an ambitious program to measure the fluorescence yield in the interval 6 kev 42 MeV using four different accelerators [53]. The interval 6 3 kev is covered by the Advanced Photon Source of the Argonne National Laboratory. The intense synchrotron X-ray flange spacer source Lead fluorescence region 5cm Electron beam Gas out PMT Scintillator Fig. 4. Schematic drawing of the chamber (top view) used by Nagano et al. [46]. Three photomultipliers are mounted on two sides and the top of the chamber, they view fluorescence light through quartz windows. Optical filters are mounted between the photomultipliers and the windows. Electrons from a 9 Sr radioactive source are beamed and detected by a scintillation counter.

9 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) times are needed to achieve sufficient statistics, then increasing systematic uncertainties. In the last years, sources with increasing activity have been used. Nagano et al. [46,47], using a 3.7 MBq 9 Sr source, were able to measure the absolute value and the pressure dependence of fluorescence for isolated bands using broadband 1 nm filters. A source of 37 MBq has allowed Waldenmaier et al. [5] (AIRLIGHT experiment) accurate measurements of the very short nitrogen lifetimes in air at high pressure. The most active source ever used in this field is the one of Lefeuvre et al. [54] with an activity of 37 MBq which has allowed to record the spectrum with a monochromator of 6 nm resolution. Finally, the MACFLY Collaboration also used a 9 Sr source for measurements of the absolute fluorescence yield at 1.5 MeV [52]. Alpha emitters are also a very useful tool for fluorescence studies. As an example, an interesting study on pure nitrogen using a 241 Am source of 3.7 kbq has been carried out [41]. Alpha particles lose energy by excitation and ionization in the gas. Although direct excitation of the N 2 2P system is forbidden, low-energy secondary electrons excite the C 3 P u upper level (see Ref. [41] for more details). Many important properties of air fluorescence like its dependence on pressure, temperature, and humidity can be studied using this technique. Again, the main disadvantage is the low fluorescence intensity due to the limited source activity which in this case might be more important for legal restrictions of alpha sources. Fig. 5. Thick-target configuration of the FLASH Collaboration showing a GEANT3.2 simulation of an electromagnetic shower generated in the target [58,59] Low-energy electron guns. Air-fluorescence emission induced by low-energy electrons ðeo:1 MeVÞ is of great interest. In the first place, a non-negligible fraction of the energy deposited in the atmosphere by a cosmic-ray shower is delivered by lowenergy electrons [9]. Furthermore, the assumption of proportionality between fluorescence intensity and deposited energy might not be fulfilled at low electron energies [55]. Customized electron guns are being used for this application. Morozov et al. [56] employ a modified electron gun designed for monochrome displays. The cathode is operated at high negative potential and the anode is connected to the ground. The gun delivers electrons of about 12 kev. Electron pulses of about 5 ns FWHM are performed by means of the control grid of the electron gun. Rosado et al. [57] have designed a novel gun. The electron emission is based on a plasma produced by a pulsed nitrogen laser focused on the cathode, with up to 3 Hz repetition rate. The cathode, which is maintained at a negative potential by a high voltage power supply, accelerates electrons to kinetic energies up to 3 kev. Electron pulses of about 2 ns width and 4 ma peak intensity are achieved using this technique. For fluorescence studies at high pressure induced by lowenergy electrons, a very thin window has to be used to isolate the electron gun from the collision chamber. Morozov et al. use an ultra thin (3 nm) silicon nitride window which allows the passage of 12 kev electrons without substantial energy degradation. For the moment, Rosado et al. are working at low pressure. Differential pumping allows maintaining pressure in the electron gun well below.1 Pa to ensure cathode isolation, whereas working pressures up to 35 Pa can be used in the gas cell The target Concerning the target two types of fluorescence experiments are being carried out. The so-called thick-target and thin-target experiments. For high-energy electrons ðe\1 MeVÞ, air can be considered a thin target since the attenuation of the beam is very small even at atmospheric pressure. Most experiments described here are carried out under thin-target conditions (e.g. the Nagano experiment shown in Fig. 4). In our field thick-target experiments are those which use a dense medium where the high-energy electrons initiate an electromagnetic shower which enters the air collision chamber to produce fluorescence light. In other words, in these thick-target experiments the fluorescence light produced by an electromagnetic shower (created in a thick non-air target) on a thin air target is studied. Two experiments have used the thick-target technique, FLASH and MACFLY. A schematic view of the thick-target configuration of the FLASH Collaboration is displayed in Fig. 5. The result of a GEANT3.2 simulation of an electromagnetic shower generated in the target is shown [58,59]. The electron beam is incident on a variable-thickness ceramic alumina stack. This material has good thermal properties along with possessing a critical energy similar to that of air. The MACFLY thick device [6] is composed of an internally black covered quasi-cylindrical, large volume ð 1m 3 Þ, pressurized tank containing the gas under study. The electron beam, aligned with the axial symmetry of the chamber, is impinging on a pre-shower target. This variable-thickness pre-shower system is used to initiate electromagnetic showers inside the chamber. A particular case is an air target at very low pressure ðo35 hpaþ for the study of the fluorescence contribution of secondary electrons as used by Rosado et al. [57]. The experimental conditions, i.e. low pressure and low energy ð3 kevþ are suitable for the analysis of spatial features of the fluorescence emission. This experiment has allowed to test the results of a model [55], discussed below in Section 4.2.1, for the calculation of the fluorescence light generated by secondary electrons. The accurate knowledge of the dependence of fluorescence intensity on environmental conditions is one of the most important goals in this field. The gas target where fluorescence is produced in the laboratory is in general a mixture of gases emulating air under various atmospheric conditions. Since airfluorescence light is basically produced by nitrogen, many

10 1 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) 1 22 Fig. 6. The temperature chamber used by the AIRFLY Collaboration [44]: (a) the chamber at the beam line as it appears before mounting the polystyrene box, (b) the chamber inside the polystyrene box, with a protective drum and pipe also in place. experiments have been performed using pure nitrogen as target. Fluorescence in air is strongly quenched by oxygen collisions while pure nitrogen is much more efficient. Thus, properties of N 2 fluorescence can be more easily studied using pure nitrogen. Several experiments have been carried out to check the effect of argon on air fluorescence (e.g. Ref. [32]). The effect of humidity has been studied as well [44,49,5,56,61], adding to the mixture a known amount of water vapor. Another very important parameter is the air temperature. The dependence of fluorescence yield on temperature in a large interval, covering that found in the atmosphere, is an experimental challenge. Devices capable to provide air targets under controlled temperatures in the required interval have been designed by AIRFLY [44] (Fig. 6) and Fraga et al. [41]. See these articles for details on the chamber design Detection techniques The detection and analysis of the air-fluorescence radiation are carried out using the appropriate optical and electronic devices. In the first place, the emitted fluorescence light has to be collected and, if possible, spectroscopically analyzed. For the latter task, a set of filters or a monochromator are used. For interference filters the dependence of the spectral response on the incident angle has to be carefully measured [41,5,62]. If sufficient fluorescence intensity is available, a monochromator can be used to measure the fluorescence spectrum [32,54,57]. The spectrum provides a measure of the relative intensities which is a very valuable information. In addition, the dependence on pressure of either reciprocal lifetimes [5] or intensities [32,47] of spectroscopically resolved fluorescence yield allows to measure the P v values. For the detection of fluorescence light, the most usual tool is a photomultiplier working in single photon counting regime. In fact, if possible, several photomultipliers viewing the collision chamber from several viewpoints allow a higher efficiency and the possibility to record simultaneously the fluorescence radiation in different spectral intervals. The AIRFLY Collaboration uses additionally a hybrid photodiode capable of single photoelectron counting [62] Absolute calibration The most important objective of this world-wide effort is an accurate measurement of the absolute value of the air-fluorescence yield. For this task, it is necessary to calibrate the detection system absolutely, including geometrical and transmission factors of the entire optical system. The absolute value of the number of electrons traversing the field of view of the collision chamber has to be measured. Fig. 7. Experimental set-up used by the AIRFLY Collaboration for the measurement of the absolute air-fluorescence yield [62]. To determine the fluorescence yield, the energy deposited by the electron beam inside the volume observed by the optical system has to be known. A first approach, which might be valid at low electron energy is to assume that the energy loss, as predicted by the Bethe Bloch formula, equals the energy deposited by the electrons in the medium [45,46]. As discussed later, secondary electrons generated by the primary electron are mainly responsible of both the fluorescence emission and the energy deposition in the medium. Therefore, the total size of the volume where energy is deposited (and fluorescence is emitted) is related to the range of secondary electrons. For high-energy primaries, a non-negligible fraction of the energy is deposited by secondaries with a range larger than the typical size of the experimental collision volume observed by the optical system. In this case, a Monte Carlo simulation is very useful to determine the energy deposited in the interaction region accurately, including the geometrical features of the collision chamber and the optical field of view. Several standard Monte Carlo codes, like EGS4 [63] and GEANT4 [64] are being used for this purpose. Several techniques have been developed for the absolute calibration of the optical systems. In principle, an accurate measurement of the geometrical features of the electron beam, the collection system, the transmission of all the optical elements, and the quantum efficiency of the light detector provide the necessary efficiency factor. This procedure has been applied by several experiments [47,5,52,54].

11 F. Arqueros et al. / Nuclear Instruments and Methods in Physics Research A 597 (28) Other calibration procedures have been developed in order to reduce the (usually large) systematic uncertainties from the efficiency parameters mentioned above. These techniques rely on the comparison of fluorescence intensity with a well-known physical process leading to the emission of light with the same spectral and geometrical features. Two physical processes have been employed for this purpose. The first one uses the Cherenkov light emitted by the electron beam in the gas, while the second one is based on Rayleigh scattering from a laser beam replacing the electron beam. The AIRFLY Collaboration [62] has developed the technique based on the comparison with Cherenkov light. The measurements are taken in two modes (Fig. 7). In the fluorescence mode, the isotropic fluorescence light produced by the electrons in the field of view of the detector is recorded. In this mode, contributions from other sources of light, like Cherenkov or transition radiation, are negligible due to the non-isotropic emission of such mechanisms. In the Cherenkov mode, a thin mylar mirror at an angle of 45 is inserted remotely into the beam, redirecting the Cherenkov light into the detector. In this mode, the Cherenkov light fully dominates over fluorescence. The absolute fluorescence yield is then determined using the ratio of the signal measured in the fluorescence and in the Cherenkov configurations. The Cherenkov yield is known from theory, the geometrical factors of the apparatus are derived from a full GEANT4 simulation of the detector and take into account the probability of a photon being emitted in each case and also the fact that Cherenkov light is very directional and fluorescence light is emitted isotropically. Using this technique, the AIRFLY Collaboration has measured the absolute yield of the 337 nm band. A preliminary result has been presented already in Ref. [62]. The technique based on a comparison with the Rayleighscattered light was proposed by the FLASH and the Madrid groups at a previous workshop [65]. A nitrogen pulsed laser beam crosses the collision chamber in the place of the electron beam. Typical pulses of about 1 mj energy and 4 ns width scatter a number of photons of the same order of magnitude as those from fluorescence runs. One of the main problems of this technique is light scattered at the walls of the chamber which has to be carefully suppressed. A measurement of the pressure dependence of the Rayleigh signal provides valuable information on the background scattered light and the linearity of the signal. Using this technique, the FLASH Collaboration has already carried out a measurement of the absolute yield with an uncertainty below 1%. The Madrid [57] and AIRLIGHT [5] groups are presently using this technique for the absolute calibration of their systems. Two different strategies are being used for the measurement of the total fluorescence yield in the spectral interval of the telescopes. Several experiments [47,52,54] carry out an absolute measurement of the yield for the whole spectral interval including many molecular bands while Ref. [62] measures the absolute fluorescence yield of the main band (337 nm) and the contribution of the remaining spectral components is inferred later from an accurate measurement of the spectrum [32]. Notice that a comparison of results of the fluorescence yield in different spectral intervals needs a value for the relative intensities as well as the P v values, see Eq. (11) Theoretical approaches Predictions on fluorescence emission The well-known physical processes leading to molecular excitation and fluorescence emission have been described in Section 3. Einstein coefficients, Franck Condon factors as well as Fig. 8. The energy loss of a primary electron in DX gives rise to the production of secondaries, being mainly responsible for the fluorescence light emission. A fraction of both deposited energy and fluorescence emission might take place outside the observation region [55]. excitation and ionization cross-sections are available in the literature, e.g. Refs. [35,36]. The amount of fluorescence photons generated by electrons traversing a given air thickness has been calculated in Refs. [33,34] using a Monte Carlo algorithm which takes into account the dominant role of secondary electrons. This algorithm also calculates the energy deposition for which secondary electrons are mainly responsible. Bunner [16] realized early that secondary electrons from ionization processes are the main source of fluorescence light, since the excitation cross-section of the corresponding upper levels (Fig. 3) shows a fast decrease with energy, in particular the one for the 2P system. Unfortunately, Bunner [16] was not able to calculate the fluorescence emission from secondary electrons since the necessary data, in particular, the spectrum of secondary electrons were not available at that time for collisions at high energy. An estimate of the energy spectrum of secondary electrons up to the GeV range has been used in Refs. [33,34] to calculate for the first time the fluorescence intensity induced by high-energy electrons. An improved energy spectrum of secondaries has allowed recently more reliable results of the fluorescence intensity and also a precise calculation of deposited energy and, thus, of the fluorescence yield [55]. A schematic view of the processes involved in the emission of fluorescence light and the deposition of energy from secondary electrons as modeled in Ref. [55] can be seen in Fig. 8. A primary electron traversing an atmospheric depth DX may either excite or ionize a molecule. In the latter case, the secondary electron produces further excitations and/or ionizations until all secondaries are stopped in the medium. Both fluorescence generation and energy deposition due to molecular excitations/ionizations are calculated using a Monte Carlo algorithm. As a result, the energy deposited per unit path length of air as well as the number of molecules excited to the upper levels of the 2P and 1N system are determined. The results for both magnitudes depend on the volume of the interaction region as well as the air pressure. In fact, it is a function of P R, where R is the radius of the sphere around the interaction point defining the medium size. Neglecting the quenching effect, the ratio of both magnitudes gives Y, i.e. the fluorescence yield at P ¼. Results on these predictions are compared with experimental data in Ref. [55]. The predicted values of the energy deposited per unit path length as a function of electron energy for several values of P R are depicted in Fig. 9 [55]. As expected, deposited energy at very high P R values tends to the total energy loss predicted by the Bethe Bloch theory. Notice that for typical observation volumes in